SPATIAL STOCHASTIC MODELS AS A POWERFUL TOOL FOR UNCERTAINTY MODELING IN HETEROGENEOUS RESERVOIR FORMATIONS

Quantitative geological and petrophysical models which integrate all available information and realistically reproduce the geologic formation heterogeneities are determinant in the proper modeling of fluid flow and transport mechanisms in oil reservoirs. In particular, modeling the spatial distribution of formation heterogeneities in a static reservoir characterization is a crucial and difficult task due to the lack of data and hence its degree of uncertainty. For this reason, during the past 15 years stochastic models to simulate the spatial distribution of facies and petrophysical properties have been applied.

In this work two novel sthocastic methods in the framework of geological and petrophysical reservoir modeling are presented. The first one is a surface based sthocastic method with geological oriented process approach for complex arquiecture modeling in turbidite sedimentary formations. Whereas the second one is a copula based stochastic method for joint modeling of complex dependencies in petrophysical properties (porosity, permeability, etc) for naturally fractured carbonate formations.

The surface based stochastic method is applied to model chronostratigraphic surfaces for turbidite lobe systems in 2D. Here, surfaces are simulated using the logic of chronological sedimentation processes, considering a lobular geometry as the basic architectural element. The simulation method is based on parametrized surface template, in which the frequency, shape, dimension and height of lobes are controlled by user-specified probability distributions.

The copula based stochastic method basically consists on applying the simulated annealing method with a joint probability distribution model estimated by a non parametric Bernstein copula. This approach has several advantages, among others we can mention that does not require the assumption of normality or other probability distribution, and is not restricted to the case of linear dependence between the variables.

The performance of both methods applied to reservoir case studies is shown.